Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Average Accuracy: 83.6% → 98.2%

Time: 14.6s

Precision: binary64

Cost: 704

Math

\[x + \frac{y \cdot \left(z - t\right)}{z - a} \]

↓

\[x + \frac{y}{\frac{z - a}{z - t}} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))

↓

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- z a) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

↓

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((z - a) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / (z - a))

↓

def code(x, y, z, t, a):
	return x + (y / ((z - a) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)))
end

↓

function code(x, y, z, t, a)
	return Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / (z - a));
end

↓

function tmp = code(x, y, z, t, a)
	tmp = x + (y / ((z - a) / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	83.6%
Target	98.2%
Herbie	98.2%

\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

1. Initial program 83.6%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]

2. Simplified 98.2%

   \[\leadsto \color{blue}{x + \frac{y}{\frac{z - a}{z - t}}} \]
   Proof

   [Start] 83.6	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   associate-/l* [=>] 98.2	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

3. Final simplification 98.2%

   \[\leadsto x + \frac{y}{\frac{z - a}{z - t}} \]

Alternatives

Alternative 1
Accuracy	68.9%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -820000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	69.2%
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -480000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	69.2%
Cost	980

\[\begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -51000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	69.2%
Cost	980

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -40000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	69.0%
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -230000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-298}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	73.7%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	83.1%
Cost	972

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 8
Accuracy	85.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-173} \lor \neg \left(z \leq 6 \cdot 10^{-79}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{a}\right)\\ \end{array} \]

Alternative 9
Accuracy	82.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-173} \lor \neg \left(z \leq 3.3 \cdot 10^{-76}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10
Accuracy	84.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-174} \lor \neg \left(z \leq 3.25 \cdot 10^{-80}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11
Accuracy	95.6%
Cost	836

\[\begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+143}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 12
Accuracy	78.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-70} \lor \neg \left(z \leq 1.08 \cdot 10^{-72}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 13
Accuracy	69.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Accuracy	57.0%
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Accuracy	55.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))